Fractures and vector valued maps

We study a class of non smooth vector valued maps, defined on n-dimensional domains, which allow for fractures of any integer dimension lower than n.We extend some well known features about (n−1)-dimensional jumps ofSBV functions and 0-dimensional singularities, or cavitations, of the distributional determinant of Sobolev functions. Variational problems involving the size of the fractures of any dimension are then studied